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a_b_sqrt2.py
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a_b_sqrt2.py
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import math
from typing import List
import bintrees
from test_framework import generic_test
# These numbers have very interesting property, and people called it ugly numbers. It is also called quadratic integer rings.
class Number:
def __init__(self, a, b):
self.a, self.b = a, b
self.val = a + b * math.sqrt(2)
def __lt__(self, other):
return self.val < other.val
def __eq__(self, other):
return self.val == other.val
def generate_first_k_a_b_sqrt2(k: int) -> List[float]:
# Initial for 0 + 0 * sqrt(2).
candidates = bintrees.RBTree([(Number(0, 0), None)])
result: List[float] = []
while len(result) < k:
next_smallest = candidates.pop_min()[0]
result.append(next_smallest.val)
# Adds the next two numbers derived from next_smallest.
candidates[Number(next_smallest.a + 1, next_smallest.b)] = None
candidates[Number(next_smallest.a, next_smallest.b + 1)] = None
return result
if __name__ == '__main__':
exit(
generic_test.generic_test_main('a_b_sqrt2.py', 'a_b_sqrt2.tsv',
generate_first_k_a_b_sqrt2))